Forced vibrations of multilayered cylindrical shells taking into account the discresibility of the ribs with non-steady loads

Space Technology ◽

Nonstationary Vibrations ◽

Shells Of Revolution ◽

Motion Equations ◽

Discrete Ribs ◽

Wave Problems ◽

Theory Of Shells

This work considers the problem of nonstationary behavior of multilayered discretely reinforced cylindrical shells.By the way the problem is very important. Multiplayed shells with allowance for discrete ribs are widely used in engineering, industrial and public building, aviation and space technology, shipbuilding. In the framework of the Timoshenko type non – linear theory of shells and ribs nonstationary vibrations multilayered shells of revolution with allowance for discrete ribs are investigated. Reissner’s variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance for discrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers, as well as bringing their solutions to receiving concrete numerical results in wide diapason of geometrical, physico–mechanical parameters of structures are elaborated. In particular three-layer discretely reinforced cylindrical shells were investigated.

Naukovì dopovìdì Nacìonalʹnogo unìversitetu bìoresursiv ì prirodokoristuvannâ Ukraïni ◽

A problem of non – linear deformation of five–layer conical shells with allowance for discrete ribs

10.31548/dopovidi2021.06.016 ◽

2021 ◽

Author(s):

N. V. Arnauta ◽

Keyword(s):

Shells Of Revolution ◽

Linear Deformation ◽

Conical Shells ◽

Non Linear ◽

Stationary Loading ◽

Discrete Ribs ◽

Linear Differential ◽

Wave Problems

A problem of non – linear deformation of multiplayer conical shells with allowance for discrete ribs under non – stationary loading is considered. The system of non – linear differential equations is based on the Timoshenko type theory of rods and shells. The Reissner’s variational principle is used for deductions of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance distcrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers. As a numerical example, the problem of dynamic deformation of a five-layer conical shell with rigidly clamped ends under the action of an internal distributed load was considered.

The formulation and analysis of the nine-point finite difference approximation for the neutron diffusion equation in cylindrical geometry

10.31274/rtd-180814-2761 ◽

1975 ◽

Author(s):

Hamza Khudhair Al-Dujaili

Keyword(s):

Finite Difference ◽

Diffusion Equation ◽

Cylindrical Geometry ◽

Neutron Diffusion ◽

Neutron Diffusion Equation

Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

Communications in Computational Physics ◽

10.4208/cicp.201010.090611a ◽

2012 ◽

Vol 12 (1) ◽

pp. 193-225 ◽

Cited By ~ 18

Author(s):

N. Anders Petersson ◽

Björn Sjögreen

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Half Space ◽

Material Model ◽

Second Order ◽

Space Problem ◽

Standard Linear Solid ◽

Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

Society of Petroleum Engineers Journal ◽

10.2118/1359-pa ◽

1966 ◽

Vol 6 (03) ◽

pp. 217-227 ◽

Cited By ~ 10

Author(s):

Hubert J. Morel-Seytoux

Keyword(s):

Oil Recovery ◽

Numerical Solutions ◽

Mobility Ratio ◽

Numerical Techniques ◽

Sweep Efficiency ◽

Closed Form Solutions ◽

Regular Patterns ◽

Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.